Angle Basics

Defining Angles

An angle is formed when two lines intersect at a point.
Each angle is measured in degrees.
A right angle is 90 degrees, represented by a small square in the corner.
An acute angle is less than 90 degrees, and an obtuse angle is more than 90 degrees but less than 180.
A straight angle is exactly 180 degrees and looks like a straight line.
When two straight lines intersect, they form four adjacent angles which are equal. The angles across from each other in this scenario are called vertically opposite angles.

Types of Triangles with Respect to Angles

Right-angled triangles consist of one right angle.
In acute-angled triangles all the angles are less than 90 degrees.
A triangle with one obtuse angle is called an obtuse-angled triangle.
The sum of the angles in any triangle is always 180 degrees.

Parallel Lines and Angles

Parallel lines are two lines in a plane that never meet and are at equal distances from each other.
Corresponding angles lie on the same side of the transversal and in similar positions. When the lines are parallel, these angles are equal.
Alternate angles are between the parallel lines and on opposite sides of the transversal. These are also equal when the lines are parallel.
Interior or Allied angles are between the parallel lines but on the same side of the transversal, their totals equal 180 degrees.

Working with Angles in Polygon

A polygon is any 2-dimensional shape formed with straight lines.
Regular polygons have sides that are all the same length and angles that are all the same.
The sum of interior angles in any polygon can be found by multiplying the number of triangles the polygon can be divided into by 180.
The sum of exterior angles in any polygon is always 360 degrees.

Conversions and Measuring Angles

Degrees, minutes, and seconds are the units used to measure angles, with 60 seconds in a minute and 60 minutes in a degree.
A protractor is typically used to measure angles accurately.
The units used are decimal in nature and not fractional.

Acquiring a solid grounding in the above-mentioned concepts will facilitate understanding of more complex geometric problems. Practice deriving and applying these relations to strengthen their concepts. They’re very useful in various fields, such as construction, land mapping, architecture, and more.